Question

Question:Three vessels of different shapes are filled to the same level with water as in Figure OQ14.7. The area of the base is the same for all three vessels. Which of the following statements are valid? (Choose all correct statements.) (a) The pressure at the top surface of vessel A is greatest because it has the largest surface area. (b) The pressure at the bottom of vessel A is greatest because it contains the most water. (c) The pressure at the bottom of each vessel is the same. (d) The force on the bottom of each vessel is not the same. (e) At a given depth below the surface of each vessel, the pressure on the side of vessel A is greatest because of its slop

Short answer

Option (a) is correct because, the pressure at the top surface of vessel A is greatest because it has the largest surface area.

Step-by-step solution

Step 1: Archimedes’ principle

When an object is partially or fully submerged in a fluid, the fluid exerts on the object an upward force called the buoyant force. According to Archimedes’s principle, the magnitude of the buoyant force is equal to the weight of the fluid displaced by the object:

B= ${\rho }_{Fluid}g{V}_{disp}$

Where V_dispthe volume of fluid is displaced and $\rho$_Fluid is the density of the fluid.

Find which of the following statements are valid

• ThevesselsBarenarrowestandvesselAiswidestatthetop.
• TheheightcolumnoftheliquidinvesselsBwillbemaximumandinvesselsAwillbeminimum, whenthevesselsarefilledbysamequantityofliquid.
• ThepressureduetoheightcolumnoftheliquidatthebaseismaximuminvesselsBandminimuminvesselsA
• HencetheforceatthebaseofthevesselsBwillbemaximumandthatatthebaseofthevesselsAwillbeminimum, asthebaseareaofallthevesselsisthesame
• Itwillberemainunchanged forC
• Therefore option (b) and (c) are the correct answers for this question.